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  • JD Laborada 12:33 am on May 25, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform – Image Compression 

    Fourier transform is useful for image compression. If you save the individual pixel colors less accurately, the image will look far from the original image. But if you save the spectrum less accurately, the picture just gets slightly blurry (better).

    By doing a sophisticated analysis of the way the human brain processes image data, you can estimate which frequencies in a given image are “the most important”, and store those with high precision, while throwing away any “less important” frequencies.

  • Daine Daling 5:57 pm on May 23, 2017 Permalink | Reply
    Tags: Transform   

    Fourier in Quantum Mechanics 

    Fourier transforms are used extensively in areas such as signal processing and electronics. However, Fourier analysis is also useful in quantum mechanics and quantum field theory. Because it is used in solving partial differential equations, it is useful in solving Schrodinger’s equation, as detailed here . Of course, the many applications of Schrodinger’s equations and quantum mechanics follow.

  • abcorwynd 4:46 pm on May 23, 2017 Permalink | Reply
    Tags: Transform   

    Week 4: Laplace and Fourier Transform 

    In real life, we can apply Fourier Transform in for creating terrain data in 3D manipulation that can be used for graphics in different kinds of software like gaming or mapping. Fourier Transform works by smoothening out rigid terrain to make it look more like real life terrain. As seen in these examples:

  • Jairus Garcia 2:33 pm on May 23, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform in Making Noise-less Appliances 

    Most electric appliances such as washing machines, refigerators, and dishwashers make noise and vibrations when on use. Manufacturers are trying to eliminate this problem. However, it is necessary to know the natural frequencies of vibrated system in order to make measures to reduce the vibrations. One way to accomplish this is recording sound to a digital file and transforming the data by the Fast Fourier Transformation.

    This is expounded in this paper: http://www.sciencedirect.com/science/article/pii/S1877705812045687

  • Gerald Roy Campanano 1:36 pm on May 23, 2017 Permalink | Reply
    Tags: Transform   

    Chemical Kinetics and Laplace Transform

    Chemical kinetics is the quantitative study of chemical systems that are
    changing with time. (Thermodynamics, another of the major branches of
    physical chemistry, applies to systems at equilibrium—those that do not
    change with time.)[1]

    Laplace Transforms can be used to handle moderately complicated chemical systems. But these techniques work only for linear (1st-order) systems. This can be used in handling mixed order reaction equations, such as “mixed second order” reactions.

    [1] http://faculty.gvsu.edu/mcbaneg/chm358wi02.pdf
    [2] https://math.stackexchange.com/questions/1248834/chemical-kinetics-using-laplace-transformation/1248849
    [3] http://www.biokin.com/tools/pdf/Koro11-Kinetics-Maple-Chap2.pdf

  • Ethan Tan 7:41 pm on May 22, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform Piano 

    Each key of a piano corresponds to a discrete wave form of sound. By the simple act of pressing down multiple keys simultaneously, the sound produced becomes a combination of different waves.

    • Paul Rossener 5:38 am on May 23, 2017 Permalink | Reply

      Please explain further the application of Fourier transform (e.g. why do we want to get the FT of the waves).


  • Camille Comia 8:41 am on May 22, 2017 Permalink | Reply
    Tags: Transform   

    Transform: Visualizing the Audio Spectrum 

    An application of Fourier transforms is an audio spectrum analyzer. A spectrum analyzer is used to view the frequencies which make up a signal, like audio sampled from a microphone. Let’s make the hardware visualize audio frequencies by changing the intensity of LEDs based on the intensity of audio at certain frequencies.

    The video below shows the spectrum display listening to powerful orchestral music with a sample rate of 4000 hz, 40 minimum decibels and 60 maximum decibels. You can see the effects of instruments playing at different frequencies and how the LEDs representing those frequencies respond.


  • Justo Balderas 5:56 pm on May 21, 2017 Permalink | Reply
    Tags: Transform   

    Quickly multiply two big integers via Fourier Transform 

    Week 4: Laplace and Fourier Transform

    The fastest known algorithms for the multiplication of very large integers use the “polynomial multiplication method” which uses Fourier transform. [5]


    Multiplying huge integers is an operation that occurs in many fields of Computational Science: Cryptography, Number theory, just to name a few. The problem is that traditional approaches to multiplication require O(n2) multiplication operations, where n is the number of digits. To see why, assume for example that we want to multiply the numbers 123 and 456. The normal way to do this is shown below.

    We see that for two integers of length 3, this multiplication requires 3 x 3 = 9 operations, hence its O(n2complexity. Executing an O(n2) algorithm for huge n is very costly, so that is why it is preferred to use more efficient algorithms when multiplying huge integers. One way to do this more efficient (in O(n log(n))), is by using FFT’s (Fast Fourier Transforms).[4]

    So how?

    “a number can indeed be divided on a decimal basis and the product of two of them is equivalent to the convolution product which on its turn can be handled fastly with FFT.”[3]

    1] Represent the integer as a polynomial

    2] Use the multiplication algorithm for polynomials using FFT

    3] O(n) carry-propagation step


    [1] https://www.quora.com/What-are-some-non-obvious-applications-of-the-Fourier-transform/answer/Lionel-Chiron (visited on May 21, 2017).

    [2] https://math.stackexchange.com/questions/116674/what-is-the-fastest-way-to-multiply-two-digit-numbers#comment271358_116674 (visited on May 21, 2017).

    [3] https://www.quora.com/What-are-the-major-applications-of-the-Fast-Fourier-Transform-FFT-to-algorithms-in-Computer-Science/answer/John-McGonagle (visited on May 21, 2017).

    [4] (2017). Cs.rug.nl. Retrieved 21 May 2017, from http://www.cs.rug.nl/~ando/pdfs/Ando_Emerencia_multiplying_huge_integers_using_fourier_transforms_paper.pdf

    [5] https://en.wikipedia.org/wiki/Discrete_Fourier_transform#Polynomial_multiplication (visited on May 21, 2017).
    [6] https://en.wikipedia.org/wiki/Multiplication_algorithm#Fourier_transform_methods (visited on May 21, 2017).

  • Camille Razal 1:38 pm on May 21, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transfrom in MRI 

    “Magnetic resonance imaging (MRI) is a test that uses a magnetic field and pulses of radio wave energy to make pictures of organs and structures inside the body. In many cases, MRI gives different information about structures in the body than can be seen with an X-ray, ultrasound, or computed tomography (CT) scan.”[1]

    The signals retrieved from a Magnetic Resonance Imaging (MRI) scan are “a combination of signals from all over the object being imaged.”[2] As we learned in class signals are composed of sine waves with different frequencies. The Fourier transform allows us to understand and interpret those frequencies and amplitudes. “It converts the signals from the time domain into the frequency domain and if we can separate out the frequencies we can say where we should plot the amplitudes on the image.”[2]





    [1] http://www.webmd.com/a-to-z-guides/magnetic-resonance-imaging-mri

    [2] http://www.revisemri.com/questions/kspace/fft


    photo source: https://www.quora.com/What-is-the-real-life-application-of-Fourier-transforms-and-Laplace-transforms?no_redirect=1

  • Jade De Guzman 10:57 am on May 21, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform in NMR Spectroscopy 

    Fourier Transform is used in a lot of spectroscopy and one of this is NMR spectroscopy.

    Nuclear magnetic resonance spectroscopy or also known as NMR spectroscopy is one of the research technique that utilizes magnetic properties of some atomic nuclei. This determines the chemical and physical properties of an atom and also the molecules contained inside one.

    Fourier transform is used to extract frequency-domain spectrum from the raw-time domain FID (free induction decay).

    source: https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance_spectroscopy

  • Levi De Guia 2:35 am on May 21, 2017 Permalink | Reply
    Tags: Transform   

    Does Laplace Have Le Place in Economics? 

    You may have only heard (and applied) Laplace Transform perhaps in your Mathematics subject or maybe in your Computer Networks subject, but did you know that it could be possible to apply this theory on certain stochastic and deterministic economic problems?

    “In a deterministic economic process the value of each function under consideration is known in advance at every future point of time.” These functions can be the cost per unit time period, the number of demanded units per unit time period, etc. For example, the maximized discounted value of a future cash flow existing during a given time interval, finite or infinite, would take a very simple form in Laplace terms[1]. The Laplace expression would be more involved if we are only to study the discounted value from a finite time interval [0, T] . The derived equations using the Laplace transform such as this one:


    would be of great use to variety of problems such as feedback controlled-production problems, inventory problems, etc.

    “In a stochastic economic process, the functions studied possess some property of giving uncertain outcomes.” This uncertainty stems from stochastic variables which have values that are unknown in advance. We also take note here the probability of these stochastic variables taking values within a certain interval which is the probability density function. If this probability function is time invariant, the process is stationary. After series of derivation and under the assumption that “using the expected value as suitable measure of the process result”, stochastic economic processes can be treated like deterministic processes.”[1] An example of a problem would be computing the expected present value of a season’s variational revenue flow using this derived equation:


    For the a detailed derivation and usage of Laplace transform in equation form, the source material is provided.


    [1] http://ctr.maths.lu.se/matematiklth/courses/FMAF05/media/material/grub67.pdf

  • Arlan Uy 2:41 pm on May 20, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform on measuring temperature 

    The Fourier transform converts a set of time domain data vectors into a set of frequency (or per time) domain vectors.

    To know about changes in soil temperature, we can measure the temperature of soil accordingly at different time of the day, every day for a year. We would then have a list of real numbers representing the soil temperatures.

    By plotting these readings on a line graph with the vertical y axis labelled as temperature and the horizontal x axis labelled time, we get a so called “time domain” graph. The graph that we created is then the sum of two  sinusoids or sine waves. The first sinusoid is with a frequency of one day as the temperature varies between day and night. The other sinusoid is with a frequency of one year as the temperature varies with the seasons.

    The Fourier Transform provides a means of manipulating or transforming this raw data into an alternative set of data, the magnitude of which can be plotted on a graph with differently labelled axis. Disregarding the y axis label for now, the x axis would be labelled ‘frequency’. This is in the frequency domain graph.

    This second graph looks very different than the first because it will consist of two vertical lines rising from the frequency axis, one at a frequency (or period) of one day, the other at a frequency of one year. Thus by using Fourier Transform on the raw data we have, we then extracted the most interesting facts from it – days are warmer than nights and summer is warmer than winter.

    Reference: http://nptel.ac.in/courses/117101055/cdeep%20demo%20ppt/application%20of%20fourier%20transforms.html

  • John Ramonel Roque 6:01 am on May 18, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform — Music 

    *listen to this music while reading this article, this is Fourier transform on its finest! 🙂

    Jimmy Hendrix, Steve Vai, John Mayer, BB King, and all those musicians, ever wonder how and why they sound so good? Apart from them being virtuoso’s,  their musical equipment played a big part on their genius.

    Signal Processing and Frequency Adjustments are the core of their gadgets, from their Instruments (Electric Guitars), vibrations are being passed/received on their pickups (Guitar Pickups) and in return converts these frequencies in forms that their Effects (Distortion, Overdrive,  etc.) can manipulate through Signal Processing and then passes it to the Amplifiers which again, processes these signals into sounds that we can listen to.

    And the process mentioned above uses Fourier Transform extensively.

  • Eliza Tan 12:30 am on May 17, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform and Frequency Filters 

    Fourier transform allows us to smoothen or sharpen images using filters. An image is first converted from spatial to frequency domain (high components=edges; low components=smooth regions) using Fourier transform then it is multiplied with a filter function (lowpass, highpass, bandpass filter) in a pixel-by-pixel fashion, and converted back to spacial domain.
    For example, a lowpass filter will reduce high frequencies and retain low frequencies resulting to a smoother image.


    original image

    resulting image after applying lowpass filter

  • JC Sun 10:31 am on May 16, 2017 Permalink | Reply
    Tags: Transform   

    Topic Four (Yay!) 

    Fourier Transform in Communication Systems

    The Fourier Transform is largely used in communications theory. It is essential to understanding how signals work through channels.

    Communication systems are “systems designed to transmit and receive information”. These information are transmitted using signals, and these signals are often viewed and analyzed in the frequency domain. Using the Fourier transform we can analyze these signals and the quality of these signals. We can also convert an analog system to a digital system using the the equations essential to the Fourier Transform.

    “Fourier Transform has greatly improved the way we are sending/collecting data.” For example, “when sound is recorded digitally the strength of the sound wave itself can be recorded (this is what a “.wav” file is), but more often these days the Fourier transform is recorded instead.” Later on, the Fourier transform signal is then “turned back into regular sound signal”.

    Fourier Transform is very helpful for images and sound files, like MP3s or JPEGs. It’s nice that we have these Transforms. I couldn’t imagine my phone without all my MP3 files!


  • Haifa Gaza 7:27 am on May 16, 2017 Permalink | Reply
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    Fourier Transform in Painting Authentication 

    Authenticating paintings has always been a problem in the art world especially during auctions. Usually, they rely on the opinion of art historians who specialize in that artist to determine a painting’s authenticity. Now, with Fourier transform, they are able to analyze the painting with certainty. After scanning the picture for a digital image, they convert it to a Fourier transform to filter useful information that would help them identify the painting’s elements. They are able to analyze the painting’s brushstrokes and compare it to an original artwork to determine its authenticity.

    Reference: https://www.google.com/patents/WO2001082263A1?cl=en

  • Aliya Miranda 3:17 pm on May 15, 2017 Permalink | Reply
    Tags: , Transform   

    “Laplace derived the differential equations for a thin fluid on a sphere with no vertical motion, only horizontal motions, called a barotropic model. Ocean tides are caused by the horizontal gravitational force of Moon and Sun. The Earth rotates so we have Corriolis forces. A slope in the sea-surface also causes horizontal force. Bottom friction and/or lateral eddy dissipation.” Thus you can use the equation to compute for the ocean tides.


    Source: http://wakes.uma.pt/cimar/PartII_lecture1.pdf

  • Lea Cornelio 2:45 pm on May 15, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform in X-ray Crystallography 

    A Fourier transform is performed when a monochomatic X-ray diffracts off a crystal. When the incidence angle is varied, the complete transform is produced.

    The diffraction corresponding to a diffraction vector s and a single electron at position r multiplies the amplitude of the scattered wave by a phase factor e^(−2πirs). If ρ(r) is the electron density function in the crystal, the effect on s will sum to

    F(s)=∫crystal ρ(r)e(−2πirs) dr.

    Therefore, structure factor F(s) appears as the Fourier transform of the electron density function ρ(r).

    How a monochromatic plane wave performs Fourier analysis on the electron density distribution:


  • Theo Yap 2:20 pm on May 15, 2017 Permalink | Reply
    Tags: Transform   

    “I’m in. #hackerman” 

    Fourier Transform can be used in image encryption and decryption. The method in which images are encrypted and decrypted use random phase masking.

    Two random matrices are instantiated, and these will be treated as our keys. To encrypt, image is multiplied by the first random matrix then Discrete Fractional Fourier Transform (DFRFT) of order alpha is applied (this is phase masking). The result is then multiplied with the second random matrix, then DFRFT of order beta is applied. To decrypt, one simply works in reverse. You first apply DFRFT of order beta-prime on the encrypted image then  multiply the encrypted image with the inverse of the second random matrix. Then, DFRFT of order alpha-prime is applied, after which, the result is multiplied with the inverse of the first random matrix. Basically, to encrypt, you apply some procedures, then to decrypt, you apply the inverse, cancelling out the encryption.

    This works because without the proper parameters/keys, decryption result returns noise, which an image may not be inferred from.fourier

    (image is a screenshot from the work of Mr. Ashutosh; mentioned in the sources)

    Ashutosh, D.S. (2013). Robust Technique for Image Encryption and Decryption Using Discrete Fractional Fourier Transform with Random Phase Masking. Retrieved from http://www.sciencedirect.com/science/article/pii/S2212017313005756

    Hennelly, B.M. & Sheridan, J.T. (2003). Image encryption and the fractional Fourier transform. Retrieved from http://eprints.maynoothuniversity.ie/5809/1/BH-Image-Encryption.pdf

    Sharma, P. (2013). Efficient Image Encryption and Decryption Using Discrete Wavelet Transform and Fractional Fourier Transform. Retrieved from https://arxiv.org/ftp/arxiv/papers/1401/1401.6087.pdf

  • Dana Redeña 9:00 am on May 15, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform in Submarines 

    Submarines (especially the first and early version ones) use a hydrophone, which is basically a microphone to collect sound waves underwater. And just like a regular microphone there could be all sorts of sounds and noise that you could collect. The tricky part now is to be able to filter the electrical signal output of the hydrophone in order to only listen to the sounds you want to listen to. This is especially important during battle whenever the submarine looks for enemy ships. In order to focus-in to the particular signal you are looking for, the electrical signal from the hydrophone is usually passed into several filters in order to single-out the certain frequency you want to hear (usually there are certain frequencies for each ship or submarine). The mathematical process for this analysis is the Fourier Transform and with the help of the early computers, they have used the Fast Fourier Transform algorithm in order to speed up the process.

    US Nuclear Submarines: The Fast Attack by Jim Christley https://books.google.com.ph/books?id=N1ibCwAAQBAJ&pg=PA2&source=gbs_toc_r&cad=4#v=onepage&q&f=false

  • Michelle Dela Rosa 9:30 pm on May 14, 2017 Permalink | Reply
    Tags: Transform   

    Speech recognition with Fourier Transform 

    Speech recognition is the capability of an electronic device to understand spoken words. [1]  It can be seen in devices that have options for taking in voice commands such as Apple’s digital assistant, Siri, which is voice-controlled.

    Fourier transforms are used to process the digital signals and analyze the frequencies of the speech sounds. Its output can be used to identify phonetic features [2], which in turn could be compiled and compared with a “phonetic dictionary” to identify what has been said. [3]

    Aside from speech recognition, some have also made studies on emotional recognition (related to speech recognition) that also makes use of Fourier transforms. The transforms are analyzed for emotional classification, noting the stresses in the speech that could be used to model the emotional state of a person. [4]


    [1] https://techterms.com/definition/speech_recognition

    [2] http://webservices.itcs.umich.edu/mediawiki/lingwiki/index.php/Fourier_transforms

    [3] http://www.explainthatstuff.com/voicerecognition.html

    [4] http://www.sci.brooklyn.cuny.edu/~levitan/nlp-psych/papers/koolagudi12.pdf


    Image from http://bgr.com/

  • Angel Furio 5:35 pm on May 14, 2017 Permalink | Reply
    Tags: Transform   

    Dancing with Fourier Transform 

    [dibs: Swing dance and fourier transform]

    Lindy Hop dance is a kind of a swing dance that originated in 1930s. Some people believed that Lindy hop is physics. And that it can be observed in the flow of energy in the dance, the changes in the linear and angular momentum, as well as the friction made with the floor. They say that:

    “Lindy is 50% Newtonian physics, 30% musicality and 20% magic.”

    Lindy Hop’s basic movements are pulse and bounce. In the video, fourier transform is used to analyze if you are pulsing enough during the dance. By measuring the acceleration and taking its fourier transform, one can now see if you are dancing with the beat!

    The top graph in the video shows the magnitude of acceleration as function of time in seconds.
    The middle graph shows the fourier transform of the last 8 seconds of acceleration in the graph above it.
    The bottom graph shows the transform of all the data up to that point in time.

    The frequency plot is measured in beats per minute and has a peak at 161 bpm, which is the tempo of the song! 🙂



  • Jennie Ablog 3:57 pm on May 14, 2017 Permalink | Reply
    Tags: Transform   

    Laplace transform in astronomy 

    The Laplace transform is a really powerful tool for processing and filtering data comprising of signals. A paper called On the interpretation of continuum flux observations from thermal radio source which was published in the Monthly Notices of the Royal Astronomical Society in 1974 discusses how to deduce the distribution of surface brightness of astronomical bodies from the spectrum of its total flux density by evaluating an inverse Laplace transform.

    Read the paper here: https://academic.oup.com/mnras/article-lookup/doi/10.1093/mnras/167.3.493

  • karen alarcon 11:19 am on May 14, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform on Audio Mixing and Analyzing 

    photo source: http://www.audioxpress.com/assets/upload/images/0/20160112070100_Waves-Audio-eMotionLV1LiveMixerFrontWeb.jpg

    If you are dealing with frequency analysis of the audio wave “quantitatively”, one of the best tools is FFT or Fast Fourier Transform. It is an algorithm to compute the Fourier transform equivalent of a time domain. [1]

    This highly advanced technique is very simple to understand, it simply converts a time domain function into a frequency domain function. [1]

    After audio mix down (where all sound of the instruments are cohesively combined into a single wave), the song is represented as a time domain function – as we can see that the x – axis of the wave is using a time element in hours: minutes: seconds (only minutes and seconds is used realistically). [1]

    photo source: http://img.brothersoft.com/screenshots/softimage/m/mixpad_audio_mixer-50050-1318575480.jpeg

    But time domain graph of the audio wave specially used during the mastering process of the track is simply a plot of amplitude (y-axis) versus time. Obviously you cannot see the frequencies of that wave. It is why we used FFT (Fast Fourier Transform) to convert this time domain representation into a frequency domain plot. With frequency domain, you can analyze the amplitude (y-axis) versus Frequencies. [1]

    photo source: http://static.kvraudio.com/i/b/audioxplorer.jpg

    [1] http://www.audiorecording.me/fast-fourier-transform-to-view-audio-frequency-spectrum.html

  • Lois Velasco 2:09 pm on May 12, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform in Microscopy

    In electron microscopy a lens can be placed behind a sample. Incident electron waves hit the sample and it creates scattering. Constructive interference and wave fronts are produced all over the sample (the lines on the picture). The lens gets parallel illumination and focuses it at a particular spot behind the lens. Other rays also hit the lens and each are focused at a particular spot behind the lens (the dot where intersection of lines can be seen). The spots on the back focal plane is the Fourier transform of the sample density (diffraction pattern). This will spread out again and it will interfere with other waves. Each ray represents a particular sine wave of a particular frequency; scattering at a different angle represents another. It will carry through and it will produce an image on the image plane. After it does Fourier transform, it will perform inverse Fourier transform (Fourier synthesis) wherein it will take each sine waves and add it up to reproduce the replica of the density sample. This copy can can be larger than the original sample.

    fft_electron microscope


  • Gabby Torres 5:13 pm on May 8, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform in Photoshop 

    Usually referred to as “Fourier Filters”, Fast Fourier Transforms or FFT is a plugin used in Photoshop to remove paper texture when editing a scanned photo. It helps lessen the texture of repeating patterns in a photo without losing the details unlike other tools used in Photoshop.

    You basically split an image into frequency components. The filter can remove the “peaks” based on the frequencies that make up repeating patterns. Then an inverse FFt is done to transform the image back.


  • Julius Carlo 5:10 pm on May 8, 2017 Permalink | Reply
    Tags: Transform   

    Week 4: Laplace and Fourier Transform 

    Biomass Estimation of Mixed Forest Landscape Using a Fourier Transform Texture-Based Approach on Very-High-Resolution Optical Satellite Imagery

    The paper discussed that the texture of a high resolution satellite image can yield information about the above-ground biomass(AGB) of different forest landscapes such as old-growth forests, and oil palm plantations. The AGB was assessed using Fourier Transform Textural Ordination(FOTO) method which involves both 2D Fast Fourier Transform(FFT) and ordination through Principal Component Analysis(PCA) for characterizing the structural and textural properties of vegetation.



  • Mikayla Lopez 1:42 pm on May 8, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform in Heart Rate Variability (HRV) Analysis 



    Reference: http://web.mit.edu/~gari/www/papers/GDCliffordThesis.pdf

  • Arianne Valencia 10:40 am on May 8, 2017 Permalink | Reply
    Tags: Transform   

    Fluid Mechanics 

    Dibs (:

  • Kyle Rosales 7:40 am on May 8, 2017 Permalink | Reply
    Tags: Transform   

    Bioinformatics: Multiple Sequence Alignment and the MAFFT software (Week 4: Laplace and Fourier Transform) 

    According to bioinfo.org.cn

    A sequence alignment is a scheme of writing one sequence on top of another where the residues in one position are deemed to have a common evolutionary origin.

    In oversimplified terms, if you have two strings like ASPOTATOLOL and ASDTOMATOLL, you want to align them in such a way that they are most “similar”. In sequence alignment the strings aren’t just random strings, they are representations of biological sequences like DNA.

    Analyzing the “similarities” in the DNA could give insights regarding the sequences: perhaps two similar protein sequences share similar functions? I’m not a biologist, so I’m not really sure about the applications of this in that field, however it seems to be a big thing.

    What I’m more interested on is the perspective from a Computer Science background. From what I remember in high school biology, there are different ways for genes to mutate. For example, a sequence may be inserted, deleted, repeated, or even changed completely. This adds a lot of complexity to the problem, you don’t just “move” one string against another and compare, you have to consider other mutations.

    For example, a “most similar” way of sequencing the two strings above might be:

    A S __ P O T A T O L O L

    A S D T O M A T O L _ L

    The “_” above represents an insertion. In terms of complexity the search space is really large (I don’t know how much exactly), it scales with the length of the strings. If you add even more sequences as in Multiple Sequence Alignment, it would scale even more.

    There are different ways of computing how “similar” sequences are, there may be different results depending on how you “score” similarities between them.

    Because of the huge time complexity of this problem it isn’t feasible to compute for the most optimal solution (and it’s even hard to define “optimal” in the first place), so an approximation or heuristic may be used.

    One software for Multiple Sequence Alignment is MAFFT (Multiple Alignment using Fast Fourier Transform ). The have a paper about their software and it’s performance measures (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC135756/) and their software can be downloaded for free (http://mafft.cbrc.jp/alignment/software/).

    As the meaning of the acronym implies, this software uses FFT. I don’t know the exact details, but from what I understand the process is somewhat similar to using FFT for audio compression. In audio compression, FFT can be used to identify “important” parts of a sound file, the “unimportant” parts are usually scraped with minimal loss to quality. Similarly, MAFFT uses FFT to find the “important” parts of the sequence and instead of analyzing the whole sequence the more “important” parts are analyzed since they’re much shorter than the whole string.




  • Patriz Cajaljal 4:53 am on May 8, 2017 Permalink | Reply
    Tags: Transform   

    Automatic 3D Face Recognition Using Fourier Transform 

    One of the applications of the Fourier Transform is on 3D face recognition. The profiles are stored in terms of their Fourier Coefficients in order to minimize the size of input data. Dimension can be reduced on deformed circular curves and on the properties of Fourier Transform.

    In order to minimize the input data, we compute the Fourier coefficients of the designated profiles and store it in a database, other than storing the actual points of the profile. Thus, having a database of images representing different individuals where each person is represented by two profiles stored by means of their Fourier’s.

    Reference: http://ieeexplore.ieee.org/document/5279600/?reload=true

  • Arvin Bandong 3:59 pm on May 7, 2017 Permalink | Reply
    Tags: Transform   

    Laplace Transform and MRP 

    The Laplace Transform together with Input-Output Analysis has been applied for the sake of formulating a basic theoretical description of multi- level, multi-period production-inventory systems (such as Material Requirements Planning, MRP). Lately, this research has been conducted in collaboration with the University of Ljubljana, where a number of extensions have been developed.


  • Eunice Angel Cruz 3:36 pm on May 7, 2017 Permalink | Reply
    Tags: Transform   

    Let's La-plus or La-minus Road Bumps! 

    “Traffic engineering is the application of Laplace Transform to the quantification of speed control in the modelling of road bumps with hollow rectangular shape.”

    The main use of road bumps in a road network is to calm speedy vehicles in a physical form. It’s main goal is to break the speed of vehicles in order to prevent over-speeding, and accidents as well. The geometry of road bumps are classified according to their shapes. For the study that I used as my reference, the method they made models the vehicle as the classical one-degree-of-freedom system whose base follows the road profile, approximated by Laplace Transform. Then, a traditional vibration analysis is carried out and the isolation factor is calculated.

    Try to read my reference from researchgate.net to learn more 😀 (hahahahuhu feel ko di ko maexplain ng maayos yung technical part pero ayun nga, ginagamit nila Laplace transform para makita yung effective distance between two road bumps, and para rin makatulong in controlling the speed of vehicles, reduce noise pollution due to vehicle movement and sudden break application, and maintain minimum impact on the vehicles).

    hehe :>



  • Roben Delos Reyes 8:28 am on May 7, 2017 Permalink | Reply
    Tags: Transform   

    R4 Laplace and Fourier Transform 

    Week 4: Laplace and Fourier Transform

    Give an application of either Laplace or Fourier transform in real-life.
    Laplace transform is used in the computation of radioactive decay. “Radioactive decay is the spontaneous breakdown of an atomic nucleus resulting in the release of energy and matter from the nucleus.” [1] Computing for the radioactive decay of a substance involves the use of differential equations. Using Laplace transform, which “is particularly useful in solving linear ordinary differential equations”, [2] makes the computation more manageable. [3]

    [1] Retrieved from https://www.nde-ed.org/EducationResources/HighSchool/Radiography/radioactivedecay.htm
    [2] Retrieved from http://mathworld.wolfram.com/LaplaceTransform.html
    [3] Retrieved from http://holbert.faculty.asu.edu/eee460/RadioactiveDecay.pdf

  • elkingmorado 8:25 am on May 7, 2017 Permalink | Reply
    Tags: Transform   

    Fourier transform and systems biology 

    Definition of Term(s)

    System Biology – is a biology-based interdisciplinary field of study that focuses on complex interactions within biological systems. From modelling of molecular interactions, to cell processes, to ecology, systems biology plays an important role.

    Actual Paper

    On the paper “Use of Fourier Series for Analysis of Biological Systems”, the authors used Fourier transform to analyze the respiratory and circulatory systems of anesthetized dogs. This study was conducted to indicate that Fourier analysis is a valid technique for investigation of oscillatory components of the circulatory and respiratory systems.








  • Arthur Yiu 2:59 pm on May 6, 2017 Permalink | Reply
    Tags: Transform   

    Moment (probability) and Laplace transforms

    First what is a moment? In statistics, a moment is a specific quantitative measure of the shape of a set of points. Now, here’s how the Laplace transform aid in probability.

    The Laplace transform is a holomorphic function. A holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain. This means that its domain includes complex numbers and that there exists a complex derivative for the function. A holomorphic function is infinitely differentiable and equal to its own Taylor series. As a holomorphic function, the Laplace transform has a power series representation. This power series expresses a function as a linear superposition of moments of the function. This perspective has applications in probability theory.

  • Jerico Silapan 2:20 pm on May 6, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform in Optics 

    Week 4: Laplace and Fourier Transform

    Fourier transform can be found on the Double Slit experiment performed by Thomas Young. The double slit experiment shows that light behaves like waves and not like particles. Fourier transform is involved because if a light passes through at slit, it will create a Fourier transform of the slits.

    Sources: http://w.astro.berkeley.edu/~jrg/ngst/fft/optics.html

  • Don Abril 1:59 pm on May 6, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform in Synthetic Aperture Radar Systems 

    Synthetic Aperture Radar

    A synthetic aperture radar (or simply SAR) is an imaging radar system that uses the recorded echoes of electromagnetic waves transmitted by an antenna to produce images. As an example, shown below is an image of Mount Teide in Spain, synthesized by a SAR system installed on the now-retired space shuttle Endeavour [1].


    What role does Fourier Transform play in SAR systems?

    First, we have to establish that for many applications, the measurements of a SAR system (relevant to the echoes recorded by the antenna) are taken along a more-or-less linear path, as in a case where the SAR is mounted or installed on an airplane. This way, A SAR antenna is at different points at different times during the measurement process.

    It is easy to imagine that generating an image by simply collating individual antenna measurements would result in one in which the same images are overlapping. This is where Fourier transform comes into play. ” In order to efficiently convert these measurements into a SAR image, the data are first [re-sampled] onto an equally spaced rectangular grid and then transformed into the image domain by a fast Fourier transform.” [2] This Fourier method allows the SAR system to synthesize, using the recorded information, an image that approximates what the object looks like in reality.


    1. https://en.wikipedia.org/wiki/Synthetic_aperture_radar
    2. bshttp://www.maths.lth.se/~fa/preprints/SAR_andersson_moses_natterer.pdf, (Fast Fourier Methods for Synthetic Aperture Radar Imaging, Andersson et al.)
  • Aira Pega 4:05 pm on May 5, 2017 Permalink | Reply
    Tags: Transform   

    (4) Fourier Transform in GPS Signal Acquisition 

    GPS is one of the most widely used wireless systems. A GPS receiver has to lock on the satellite signals to calculate its position. The process of locking on the satellites is quite costly and requires hundreds of millions of hardware multiplications, leading to high power consumption. [1]

    Apparently, the fastest known algorithm for this problem is based on the Fourier transform. A paper called “Faster GPS via the Sparse Fourier Transform” discussed about reducing complexity in relation with decreasing GPS power consumption.

    The algorithm reduces the locking complexity to O(n√(log n)). Further, if the SNR is above a threshold, the algorithm becomes linear, i.e., O(n). It exploits the sparse nature of the synchronization problem, where only the correct alignment between the received GPS signal and the satellite code causes their cross-correlation to spike. [1]

    [1] http://haitham.ece.illinois.edu/Papers/QuickSync-mobicom.pdf

  • Aimee Gonzales 1:08 pm on May 5, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform for Hearing Devices 


    A hearing aid has approximately 9 – 16 microphones, each receiving different sound waves. Fourier transform comes into picture when filtering out these sound waves. Hearing aids are also designed to adjust well based on the environment. That is, the sound of the person you are talking to still stands out despite despite the different noise sources in the environment (thanks to Fourier transform).


    Source: https://cadcammodelling.wordpress.com/2011/04/14/fourier-transform-and-its-applications/

  • Berna Misa 8:43 am on May 5, 2017 Permalink | Reply
    Tags: Transform   

    J4: Fourier Transform in Option Pricing 

    Fourier Transform (FT) option pricing is a standard option pricing method. But what is an option?

    An option is a financial derivative that represents a contract sold by one party (the option writer) to another party (the option holder). The contract offers the buyer the right, but not the obligation, to buy (call) or sell (put) a security or other financial asset at an agreed-upon price (the strike price) during a certain period of time or on a specific date (exercise date).

    Generally, there are two kinds of options. A Call Option and a Put Option.

    Call options give the option to buy at certain price, so the buyer would want the stock to go up. Conversely, the option writer needs to provide the underlying shares in the event that the stock’s market price exceeds the strike due to the contractual obligation. An option writer who sells a call option believes that the underlying stock’s price will drop relative to the option’s strike price during the life of the option, as that is how he will reap maximum profit.

    This is exactly the opposite outlook of the option buyer. The buyer believes that the underlying stock will rise; if this happens, the buyer will be able to acquire the stock for a lower price and then sell it for a profit. However, if the underlying stock does not close above the strike price on the expiration date, the option buyer would lose the premium paid for the call option.

    Put options give the option to sell at a certain price, so the buyer would want the stock to go down. The opposite is true for put option writers. For example, a put option buyer is bearish on the underlying stock and believes its market price will fall below the specified strike price on or before a specified date. On the other hand, an option writer who shorts a put option believes the underlying stock’s price will increase about a specified price on or before the expiration date.

    If the underlying stock’s price closes above the specified strike price on the expiration date, the put option writer’s maximum profit is achieved. Conversely, a put option holder would only benefit from a fall in the underlying stock’s price below the strike price. If the underlying stock’s price falls below the strike price, the put option writer is obligated to purchase shares of the underlying stock at the strike price. [1]

    One advantage of FT option pricing is its generality in the sense that the only thing necessary for FT option pricing is a characteristic function of the log terminal stock price. This generality of FT option pricing speeds up the calibration and Monte Carlo simulation with various exponential Lévy models. [2]




    [1] http://www.investopedia.com/terms/o/option.asp . May 5, 2017
    [2] Matsuda, Kazuhisa . Introduction to Option Pricing with Fourier Transform: Option Pricing with Exponential Lévy Models.
     December 2004  http://web.stanford.edu/~alahi/downloads/finance.pdf



  • Rafa Cantero 7:14 am on May 5, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform in measuring actual automotive mileage 

    A lot of people who buy second hand cars are usually able to gauge how much the car has been used by the amount of miles it has been driven. Most cars have a manual gauge that shows its mileage.

    However some salespeople would manually “rewind” this gauge so that it shows less miles than what the car was driven. Software has been invented that listens to a cars engine and uses Fourier Transformations to break down the engines sounds.

    From these sounds, the software will be able to accurately gauge how old the car really is and if the salesperson cheated or not.


  • Deanne Caingat 4:24 am on May 5, 2017 Permalink | Reply
    Tags: Transform   

    Laplace Transform in Two-Way Communication

    Laplace transform can be applied in two-way communication. (E.g. cell hones, FM/AM Radio). It is conducted while sending signals over any two-way communication.

    How it works?

    Information is converted into a time varying wave while being sent over a medium (such as cell phones). Through this conversion, information can then propagate. Consequently, on the receiving end, the medium’s time functions are converted to frequency functions so that the waves can be converted back and be interpreted.

  • Joshua Buslig 2:19 am on May 5, 2017 Permalink | Reply
    Tags: Transform   

    Image Compression 

    Image compression specifically JPEG uses Discrete Cosine Transform (DCT, which is the same class with Fast Fourier Transform). It converts visual signals into quantifiable data so that it can be processed for compression.

    Here is a video on how it works 😀 https://youtu.be/Q2aEzeMDHMA?t=3m19s

  • Edrich Chua 4:59 pm on May 4, 2017 Permalink | Reply
    Tags: Transform   

    Fourier transform infrared spectroscopy 

    Fourier transform infrared spectroscopy (FTIR) is a technique which is used to obtain an infrared spectrum of absorption or emission of a solid, liquid or gas. An FTIR spectrometer simultaneously collects high spectral resolution data over a wide spectral range. This confers a significant advantage over a dispersive spectrometer which measures intensity over a narrow range of wavelengths at a time.

    The term Fourier transform infrared spectroscopy originates from the fact that a Fourier transform (a mathematical process) is required to convert the raw data into the actual spectrum.


  • Abby del Castillo 3:14 pm on May 4, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform in Song Classification

    Shazam, a music recognition application, does several steps before being able to identify the title of the song a user has asked the program to recognize. It has to analyze the wave forms of the song and one of the methods they use for doing so is Fourier Transform. The following exerpt is an explanation on how it was actually used for the analysis,”The DFT is a mathematical methodology for performing Fourier analysis on a discrete (sampled) signal. It converts a finite list of equally spaced samples of a function into the list of coefficients of a finite combination of complex sinusoids, ordered by their frequencies, by considering if those sinusoids had been sampled at the same rate.”(Jovanovic, 2015). The analysis doesn’t end here but with the FFT analysis, a big part of the work has been done.


  • Paulo Santiago 1:09 pm on May 4, 2017 Permalink | Reply
    Tags: Transform   


    Seismic research uses Discrete Fourier Transform (DFT) and the Fast FT(FFT). If you look at the history of the FFT you will find that one of the original uses for the FFT was to distinguish between natural seismic events and nuclear test explosions because they generate different frequency spectra.

    The (fast) Fourier transform is used to convert the signal into the frequency domain, where convolution between two signals is obtained simply multiplying them together. Once again the Fourier Transform is used as a tool in Digital Signal Processing to perform other operations, rather than producing an end result itself.


  • Alezon Valerio 5:43 am on May 4, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform in Network Signal Processing 

    The Fourier Transform is extensively used in the field of Signal Processing.

    Fourier transform is used to filter signals by removing unnecessary noise. “The impulse in time can be thought of as an infinite sum of sinusoids at every possible frequency and the Fourier transform of the impulse is a constant with respect to frequency thus we can know how a system reacts to every possible frequency[1].” Using this, every signal input can be converted with the noise filtered out and then analyzed.

    [1] http://www.thefouriertransform.com/applications/filtering.php
    [2] https://see.stanford.edu/materials/lsoftaee261/book-fall-07.pdf

  • AF Formaran 12:24 pm on May 3, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform Applications on Quantum Mechanics


    “We introduce the concept of Fourier transforms of fractional order, the ordinary Fourier transform being a transform of order 1. The integral representation of this transform can be used to construct a table of fractional order Fourier transforms. A generalized operational calculus is developed, paralleling the familiar one for the ordinary transform. Its application provides a convenient technique for solving certain classes of ordinary and partial differential equations which arise in quantum mechanics from classical quadratic hamiltonians. The method of solution is first illustrated by its application to the free and to the forced quantum mechanical harmonic oscillator. The corresponding Green’s functions are obtained in closed form. The new technique is then extended to three-dimensional problems and applied to the quantum mechanical description of the motion of electrons in a constant magnetic field. The stationary states, energy levels and the evolution of an initial wave packet are obtained by a systematic application of the rules of the generalized operational calculus.

    Finally, the method is applied to the second order partial differential equation with time-dependent coefficients describing the quantum mechanical dynamics of electrons in a time-varying magnetic field.”

    To summarize, you use Fourier transform and its higher order integrals to analyze and map the mechanics of electrons placed in magnetic fields.

    Reference: http://imamat.oxfordjournals.org/content/25/3/241.short

  • Christine Felizardo 12:10 pm on May 3, 2017 Permalink | Reply
    Tags: Transform   

    Control systems 

    Laplace Transforms can be used in control systems.

    Control systems refer to a set of devices that directs the behavior of other devices. One might say that a control system controls other systems. A problem that can be solved by such is stated below:

    We have a particular electric motor that is supposed to turn at a rate of 40 RPM. To achieve this speed, we must supply 10 Volts to the motor terminals. However, with 10 volts supplied to the motor at rest, it takes 30 seconds for our motor to get up to speed. This is valuable time lost.

    Manipulation of such systems is made possible by converting them into something called a Laplace transform domain, so that a problem can be easily solved with integral transforms and Ordinary Differential Equations or ODEs (as changes can be visualized with these things). The math involved in a control system makes it possible for humans and even computers to manipulate control systems.


  • robbasilona 8:37 am on May 3, 2017 Permalink | Reply
    Tags: Transform   

    Machine Learning and Data Mining

    “Laplace Transforms could be used to determine the prediction and analyze the step of knowledge in databases”

    In general, Laplace Transforms could be used for trend finding and data-fitting in Machine Learning. Given that this field of CS deals with huge chunks of data, the usage of transforms is helpful for selective filtering and data-fitting. Furthermore, trend finding helps speed up the process.

  • JC Albano 6:47 am on May 3, 2017 Permalink | Reply
    Tags: Transform   

    Fourier Transform and one of its Medical Applications

    Image processing has all been used in the study of various fields ranging from biology or to more specific fields like bacteriology. In medicine however Fourier transforms can also be used in the very same image processing tech to study skin lesions. Selected colors in FT images are studied by scientists and experts alike. One specific skin lesion study is that of Melanoma, which is a type of skin cancer.

    In light with what I just cited, we can see the importance of Fourier Transforms and its application in image processing in medicine.

    You can know more about the paper I just read here: http://link.springer.com/chapter/10.1007%2F978-3-319-08491-6_16#page-1

    Which includes a more detailed explanation and dwells deeper into the properties of FT and how it is used in the researcher’s study.

  • Sig Encarnacion 2:30 am on May 3, 2017 Permalink | Reply
    Tags: Transform   


    “The Laplace transform can be applied to solve the switching transient phenomenon in the series or parallel RL,RC or RLC circuits ”

    Laplace transform saves us the hassle of solving ODEs by converting such equations into algebraic ones so they may be solved more easily.

    Fundamentals of analyzing RLC/RL/RC circuits:


    “1. Develop the differential equation in the time-domain using Kirchhoff’s laws (KVL, KCL) and element equations.


    2. Apply the Laplace transformation of the differential equation to put the equation in the s-domain.”


    3. Algebraically solve for the solution, or response transform.


    4. Apply the inverse Laplace transformation to produce the solution to the original differential equation described in the time-domain. “

    It transforms a typical KVL equation such as,


    into this,


    which, by isolating our target variable I is:


    which is a function involving only the variable s and some other constants (V0, I0, L, R, C).


    Continuing the example above with actual values of R, L,and C:http://www.dummies.com/education/science/science-electronics/analyze-an-rlc-circuit-using-laplace-methods/

  • Ryan Rivera 12:27 am on May 3, 2017 Permalink | Reply
    Tags: Transform   


    The Fourier transform is not just limited to simple lab examples. When used in real situations it can have far reaching implications about the world around us.

    Take for example the field of astronomy. Some times it isn’t possible to get all the information you need from a normal telescope and you need to use radio waves or radar instead of light. These radar signals are treated just like any other ordinary time varying voltage signal and can be processed digitally.

    One recent example of this technique was the NASA Magellan satellite which was released from the space shuttle Atlantis on 4th May 1989 and sent to Venus on a 15 month journey that took it one and a half times around the sun.

    Source: http://w.astro.berkeley.edu/~jrg/ngst/fft/astronmy.html

  • Paul Rossener 6:58 am on May 2, 2017 Permalink | Reply
    Tags: Transform   

    Brain Signal Processing 

    I am currently researching on brain-computer interfaces where I recorded students brain signals and classified them into different levels of cognitive load.

    In this study, I used Fourier transform (FFT) to convert the signals from time domain and frequency domain. Why is this important? You see, certain brain frequencies are correlated with activities. For example, alpha waves (8-13 Hz) are associated with alertness, while beta waves (14-30 Hz) are associated with high focus.

    By using Fourier transform, we are able to access a different dimension of information that is more significant for our study.




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